Remark 3.3 
The projection step (REF ) is a semi-definite program (SDP) involving \(O((n_\xi + n_\phi ) \times (n_\xi + n_\phi ))\)  variables. The complexity of interior point SDP solvers usually scales cubically with the number of variables, potentially bringing computational burden when \((n_\xi +n_\phi )\)  is large. Luckily, most high dimensional problems admit low dimension structures [1]} and such overhead is only paid at training without further operations at deployment.

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